English Medium Class 10 - CBSE Question Bank Solutions

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm² 

[use `pi = 22/7`]

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in given figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.

 [Use `pi = 22/7`]

A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point of PQ, then find the coordinates of P and Q.

Water in a canal, 5·4 m wide and 1·8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation?

Solve for x :

`1/(x + 1) + 3/(5x + 1) = 5/(x + 4), x != -1, -1/5, -4`

If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k

From a solid right circular cylinder of height 2.4 cm and radius 0.7 cm, a right circular cone of same height and same radius is cut out. Find the total surface area of the remaining solid.

Solve for x :

`1/(2x - 3) + 1/(x - 5) = 1 1/9 , X != 3/2, 5`

Solve for x

`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 2, "where x" != -1/2, 1`

If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides

Find the area of the shaded region in Fig. 3, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use π = 3.14]

If 4 tan θ = 3, evaluate `((4sin theta - cos theta + 1)/(4sin theta + cos theta - 1))`

The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find:

1) The area of the metal sheet used to make the bucket.

2) Why we should avoid the bucket made by ordinary plastic? [Use π = 3.14]

Prove that `(sin "A" - 2sin^3 "A")/(2cos^3 "A" - cos "A") = tan "A"`

In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.

`sin A = 2/3`

In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.

`cos A = 4/5`

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.

tan θ = 11

In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.

`sin theta = 11/5`

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.

`tan alpha = 5/12`

In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.

`sin theta = sqrt3/2`